In magnetic resonance imaging (MRI), compressed sensing reduces scan time with faster acquisition by measuring fewer Fourier coefficients. This produces a high-quality image with relatively lower scan time. Compressed sensing, in this case, removes the high spatial gradient parts—mainly, image noise and artifacts. For this purpose, random (incoherent) sampling patterns are optimal, so that the noise statistics follows white Gaussian distribution. Compressed Sensing acquisitions fix the physiological direction of the readout line during a single scan, so the readout line is always in one direction, e.g. left-to-right, front-to-back or head-to-feet. Current MRI scanners are able to achieve incoherent sampling pattern up to a limit. The limiting parameter is that the current scan technology acquires readout lines (one dimension in k-space) sequentially one sample after another. Acquisition of one continuous readout line is fast, while skipping samples within a single readout line does not save much acquisition time compared to the time saved for switching to different readout lines. Thus, entire continuous lines of samples are acquired, even if compressed sensing is used. Compressed Sensing acquisition speeds up acquisition time by skipping samples in directions other than the direction of the readout line, e.g. in phase-encoding, partition-encoding or time directions. Since the readout direction is fully sampled coherently, this sampling scheme does not introduce incoherence in the readout direction. Nevertheless, randomly sampling in the readout direction does not save acquisition time.
Non-Cartesian sampling patterns avoid this issue by relaxing the sampling frequency grid. However, non-Cartesian sampling patterns require higher computation time due to the non-uniform fast Fourier Transform (FFT) used during image reconstruction.